{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5d904dee",
   "metadata": {},
   "source": [
    "# An advanced example of lock: Symmetric functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6465ec94",
   "metadata": {},
   "source": [
    "## In this example, we will consider fitting a symmetric function which we know in a prior that it is symmetric wrt to input variables, so we want to build in this symmetry into KAN.\n",
    "$f(x,y)=xy + {\\rm exp}({\\rm sin}(\\pi x)+{\\rm sin}(\\pi y))$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94056ef6",
   "metadata": {},
   "source": [
    "### intialize model and create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0a59179d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from kan import KAN, create_dataset\n",
    "import torch\n",
    "\n",
    "# initialize KAN with G=3\n",
    "model = KAN(width=[2,3,1], grid=5, k=3)\n",
    "\n",
    "# create dataset\n",
    "f = lambda x: x[:,[0]]*x[:,[1]] + torch.exp(torch.sin(torch.pi*x[:,[0]])+torch.sin(torch.pi*x[:,[1]]))\n",
    "dataset = create_dataset(f, n_var=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb1f817e",
   "metadata": {},
   "source": [
    "### Train KAN and plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a87b97b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.08e-02 | test loss: 1.31e-02 | reg: 9.98e+00 : 100%|█| 20/20 [00:0\n"
     ]
    }
   ],
   "source": [
    "model.train(dataset, opt=\"LBFGS\", steps=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3f1cfc9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11534d3b",
   "metadata": {},
   "source": [
    "### Even without knowing this function is symmetry wrt x & y, KAN diagrams clearly display such symmetry. We can now lock visually similar activation functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0021f36b",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(3):\n",
    "    model.lock(0,[[0,i],[1,i]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "350b190a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01a946b1",
   "metadata": {},
   "source": [
    "### notice the number besides the lock symbols, indicating which locked group it belongs to. We now retrain the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8e1516fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 7.19e-03 | test loss: 7.77e-03 | reg: 9.79e+00 : 100%|█| 20/20 [00:0\n"
     ]
    }
   ],
   "source": [
    "model.train(dataset, opt=\"LBFGS\", steps=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c407b8d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe65b6ed",
   "metadata": {},
   "source": [
    "### unfortunately, the model does not appear to be very symbolically interpretable immediately. We can snap the two osciallatory functions to be sine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "28ecb6bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r2 is 0.9993783951693728\n",
      "r2 is 0.999415962003563\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor(0.9994)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fix_symbolic(0,0,1,'sin')\n",
    "model.fix_symbolic(0,1,1,'sin')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "eae7262e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.01e-03 | test loss: 1.07e-03 | reg: 1.01e+01 : 100%|█| 50/50 [00:1\n"
     ]
    }
   ],
   "source": [
    "model.train(dataset, opt=\"LBFGS\", steps=50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "71182556",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "011a9982",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = KAN(width=[2,3,1], grid=20, k=3).initialize_from_another_model(model, dataset['train_input'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "155935b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 4.81e-04 | test loss: 6.75e-04 | reg: 1.01e+01 : 100%|█| 50/50 [00:2\n"
     ]
    }
   ],
   "source": [
    "model.train(dataset, opt=\"LBFGS\", steps=50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c60e821",
   "metadata": {},
   "outputs": [],
   "source": [
    "# It shouldn't be purple. Copy is wrong."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0aa320d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5d13a66a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "function , r2\n",
      "cosh , 0.999970130164825\n",
      "gaussian , 0.9999521805509436\n",
      "tanh , 0.9999103486961142\n",
      "sigmoid , 0.9999080213847577\n",
      "exp , 0.999633407605388\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "('cosh',\n",
       " (<function kan.utils.<lambda>(x)>, <function kan.utils.<lambda>(x)>),\n",
       " 0.999970130164825)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.suggest_symbolic(1,1,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44eced8e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
